(Just going to copy and paste what I said to someone earlier, sorry.)
It’s kind of an example of Theseus’ Ship, except with his mind. If all the components have been replaced, can Uldren’s mind really still be Uldren? Yes and no. No in terms of physicality, as every piece, or “board”, of Uldren’s mind has been replaced with Crow’s mind. Yes, as the basis of the original boat still being the boat now, is up to the people who believe either way. In other words, if other people believe that it is the same ship/mind, it is the same ship. If they do not, they do not, as it is the attachment that makes something worth something to someone.
So it is up to us. Crow/Uldren said that he never wants Uldren to come back (“Uldren is dead”), however obviously any level of faith has to come into play for someone to believe something. I genuinely believe that Crow is Crow, and equally a good guy, however Uldren has deceived Guardians in the past. We just have to believe he isn’t Uldren anymore.
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So that paradox does have a purpose...
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Not entirely a paradox, but it is a good way of thinking when talking about replacing/renewing something that may have grown old or bad.